How do I eliminate a harsh lighting issue on my cylindrical glossy model?
It appears that you are using a Subsurf modifier, and a flat many-edged face on the back. That would be called an N-Gon, and is highly frowned upon in Blender as it brings a host of issues into the picture. Quads (faces with 4 edges) are much prefered, as it they work best for almost all of the relevant calculations done by Blender.

This particular issue can be resolved by adding an edge-loop near the face on the back by pressing Ctrl+R